• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Position to momentum space in three dimensions

  • Thread starter Cleo
  • Start date
Problem Statement
Mathematical complication solving Q.M. problem.
Relevant Equations
Im [(ip/ħ-1/a)^(-2)]
Hi! Im trying to change the hydrogen ground state wave funcion from position to momentum space, so i solved the integral
∫∫∫e^(prcosθ/ħ) e^(-r/a) senθ r^2 dΦdθdr
and got 4πħ(2πħ)^(-3/2) p^(-1) (πa^3)^(-1/2) Im [(ip/ħ-1/a)^(-2)], which according to the professor's solution is ok, but then i dont know wich is the imaginary part that i need to pick. p is the momentum, i is the imaginary unit, a is Bohr radius, r is the radial coordinate, and Im means imaginary part of what is in the brackets.
So basically mi question is: How do i separate the imaginary part from the real part in this expression?:

The professor said that the final result is Ψ(p)=(8πħ^4)/[(2πħ)^(-3/2) a^2 (4πa)^(1/2) (p^2+ħ^2/a^2)^2], but i have no clue of how he did that final step. I guess it shouldnt be very difficoult but i have been long trying to figure out how to do it and for some reason i dont get it. It would be very nice if some of you could help me. Thanks!


Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
To get ##i## out of the denominator, multiply the top and bottom by the complex conjugate:
$$\frac{1}{a+bi} = \frac{a-bi}{(a+bi)(a-bi)} = \frac{a}{a^2+b^2} - i \frac{b}{a^2+b^2}$$
Ahhh thanks a lot!

Want to reply to this thread?

"Position to momentum space in three dimensions" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving